I'll second this. I took my bike COMPLETELY apart over the winter and relubed everything. Just make sure to keep everything in order. Take digital pics and label everything in zip bags if necessary.
Working on a section at a time is better than just ripping everything apart at once.

Setting the races for the wheel bearings was a little tough. The races are more of a "by feel" thing but but there are videos on youtube that can point you in the right direction.
You can get a decent tool kit from Performance Bike for about $50 with everything you'll need. The only thing I needed to buy extra was a Suntour freewheel tool. $6 at my local bike shop.
An ultrasonic cleaner is great for clearing the old grease out of the bearings. You'll be amazed at what new grease can do!

Go slow and check out the Youtubes!